Analysis of homoclinic bifurcation in a nonlinearly damped duffing-van der Pol oscillator under the excitation of two-forcing terms

S. Valli Priyatharsini; L. Ravisankar; V. Chinnathambi; S. Rajasekar

S. Valli Priyatharsini Sadakathullah Appa College,\\ Tirunelveli-627 011, Tamilnadu, India
L. Ravisankar Sri K.G.S. Arts College,\\ Srivaikuntam-628 619, Tamilnadu, India
V. Chinnathambi Department of Physics, Sadakathullah Appa College, Tirunelveli-627011, Tamilnadu.
S. Rajasekar Bharathidasan University,\\ Tiruchirapalli 620 024, Tamilnadu, India

Abstract

The occurrence of homoclinic bifurcation in a nonlinearly damped Duffing-vander Pol (DVP) oscillator under the excitation of two-forcing terms with different frequencies $(\Omega,\omega)$ is analyzed with both analytical and numerical techniques. For our study, we consider two periodic \mbox{cosine} waves and two modulus of \mbox{sine} waves with different frequencies. We assume that the nonlinear damping term is proportional to the power of velocity $(\dot{x})$ in the form $|\dot{x}|^{P-1}$. Applying the Melnikov analytical technique, the threshold condition for the occurrence of horseshoe chaos is obtained for each excitations. Melnikov threshold curves, separating the chaotic and nonchaotic regions are obtained. The chaotic features on the system parameters are discussed in detail. Numerical results are given, which verify the analytical ones.